Predicting QSO Continua in the Lyα Forest

We present a method to make predictions with sets of correlated data values, in this case QSO flux spectra. We predict the continuum in the Lyman-Alpha forest of a QSO, from 1020 -- 1216 A, using the spectrum of that QSO from 1216 -- 1600 A . We find correlations between the unabsorbed flux in these two wavelengths regions in the HST spectra of 50 QSOs. We use principal component analysis (PCA) to summarize the variety of these spectra and we relate the weights of the principal components for 1020 -- 1600 A to the weights for 1216 -- 1600 A, and we apply this relation to make predictions. We test the method on the HST spectra, and we find an average absolute flux error of 9%, with a range 3 -- 30%, where individual predictions are systematically too low or too high. We mention several ways in which the predictions might be improved.